The actual "Hays Production Code for Motion Pictures" (the Hays Code) went into effect in 1934, after the Catholic Legion of Decency initiated its own system of rating content (A for acceptable, B for objectionable, and C for condemned), a much simpler and draconian matter than the various Hays Office guidelines. While it didn't kill movies to "have the fun taken out", there's something a little special about those pre-Code talkies, when writers, directors, and actors found subtle ways around the looser restrictions. For example, some dialogue from Night After Night featuring Mae West, who seemed sometimes Hays-proof:

And even while the Code was up and running, there was no way to censor a subtly-executed subtext within the hyperchaste, hypermoral Code-compliant exterior of a film. The actual enforcement mechanism for the Code was the Production Code Administration Office, run by Joseph Breen; so it was really the "Breen Office", and eventually became known as such.

With the advent of television after WWII, competition caused the film industry to loosen up, little by little, much as Standards and Practices in broadcast TV have had to adjust to the competition of premium cable in recent decades. Supreme Court rulings defended the First Amendment rights of filmmakers, making the Code pretty much a dead duck, but it would remain nominally in effect until the MPAA came up with the original version of its current rating system in 1968 (see: Rated X).